Physics in Flatland
Jim Eisenstein
Edwin Abbott Abbott
1884
A confession…
I am
a
condensed matter physicist.
A confession…
I am
a
condensed matter physicist.
Condensed matter
Not condensed matter
The Essence of Condensed
Matter Physics:
The Essence of Condensed
Matter Physics:
whole > Σ (parts)
The Essence of Condensed
Matter Physics:
whole > Σ (parts)
“Emergent” phenomena
1 neuron
1 neuron
??
100 billion neurons
1 electron
1 electron
??
100 billion electrons
Fractional quantum Hall liquid
An Hoary Example: Superconductivity
Onnes, 1911
Not so useless after all…
Two-Dimensional Electron Gas
Two-Dimensional Electron Gas
A Semiconductor Sandwich
A
B
~100 Å
A
Quantum Confinement
Electron Quantum Wave
~100 Å
Perfect Registry
~100 Å
Molecular Beam Epitaxy
“spray painting with atoms”
Molecular Beam Epitaxy
“spray painting with atoms”
heated cells
Ga
Al
As
AlGaAs
100 A
GaAs
AlGaAs
ultra high
vacuum
allows for precision
engineering of crystal
layer by layer
high quality
GaAs substrate
hot!
The final product
Two-Dimensional Electron Gas
2D Electrons in a Magnetic Field
Magnetic Field, B
Why Magnetic Fields?
No magnetic field
Big magnetic field
Magnetic field enhances COLLECTIVE behavior
Low temperatures
+5o C
Really low temperatures!
15 mK
1 meter
T = 15 mK = -273.15 °C + .015 °C
ABSOLUTE ZERO
Big magnetic fields
Really big magnetic fields!
B
B ~ 150,000 Gauss ~ 500,000 x Earth’s Magnetic Field
1998 Nobel Prize in Physics to Tsui, Stormer and Laughlin
Independent Electrons
A New Phase of Matter: The Fractional Quantum Hall Liquid
Scuba Diving in the Fractional Quantum Hall Sea
Scuba Diving in the Fractional Quantum Hall Sea
T=0
B = Bc
A featureless liquid.
No individual electrons visible!
Scuba Diving in the Fractional Quantum Hall Sea
T > 0 or B = Bc ± δB
Weird New Particles
+e/3
-e/3
Particles with fractional charge!
Really Weird New Particles!
+e/3
-e/3
Particles with fractional charge and fractional statistics!
Ψ →
i
π
/
3
e
Ψ
Anyons
Only Two Kinds of Particles in Nature:
Bosons and Fermions
Enrico Fermi
electrons, protons,
neutrons, etc.
Obey Pauli Exclusion
Principle
Satyendranath Bose
photons, mesons, etc.
Don’t!
A vanity of three dimensions…
Trading Places and Braiding Your Hair
Trading Places and Braiding Your Hair
T:
Trading Places and Braiding Your Hair
T2 :
Trading Places and Braiding Your Hair
T2 :
In 3 dimensions T2 = 1
T = +1 or T = -1
Trading Places and Braiding Your Hair
T2 :
In 3 dimensions T2 = 1
T = +1 or T = -1
BOSONS
FERMIONS
2D is Different: Trading vs. Braiding
Arrow of Time
2D is Different: Trading vs. Braiding
Arrow of Time
T
2D is Different: Trading vs. Braiding
Arrow of Time
T2
Tangled!
T2 ≠ 1?
Does braiding matter in the real world?
In Fractional Quantum Hall Land:
YES
If that isn’t bad enough: Braiding is Non-Abelian!
They may look the same, but in the
2D quantum world they may be different!
Is it good for ANYTHING?
=
A QUANTUM COMPUTER
Thanks for listening!